Threshold Policies with Tight Guarantees for Online Selection with Convex Costs
Xiaoqi Tan, Siyuan Yu, Raouf Boutaba, Alberto Leon-Garcia

TL;DR
This paper introduces simple threshold policies with tight optimality guarantees for online selection problems involving convex costs, applicable to various online resource allocation scenarios.
Contribution
It develops and analyzes threshold policies that are provably optimal among deterministic algorithms for online selection with convex costs, including bounds for randomized algorithms.
Findings
Threshold policies achieve asymptotic optimality in competitive ratio.
Lower bounds established for randomized algorithms' performance.
Generalizes online search, pricing, and auction problems.
Abstract
This paper provides threshold policies with tight guarantees for online selection with convex cost (OSCC). In OSCC, a seller wants to sell some asset to a sequence of buyers with the goal of maximizing her profit. The seller can produce additional units of the asset, but at non-decreasing marginal costs. At each time, a buyer arrives and offers a price. The seller must make an immediate and irrevocable decision in terms of whether to accept the offer and produce/sell one unit of the asset to this buyer. The goal is to develop an online algorithm that selects a subset of buyers to maximize the seller's profit, namely, the total selling revenue minus the total production cost. Our main result is the development of a class of simple threshold policies that are logistically simple and easy to implement, but have provable optimality guarantees among all deterministic algorithms. We also…
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Taxonomy
TopicsOptimization and Search Problems · Advanced Bandit Algorithms Research · Auction Theory and Applications
